Newton-Verfahren f(x) = exp(x^2)-1, x_0= 2 k |f(x_k)| x_k |x_k-x_*| conv_lin conv_quad ------------------------------------------------------------------------ 0 5.35982e+001 2.00000 -- -- -- 1 5.35982e+001 1.75458 1.75458e+000 8.77289e-001 4.38645e-001 2 2.07268e+001 1.48273 1.48273e+000 8.45061e-001 4.81632e-001 3 8.01128e+000 1.18293 1.18293e+000 7.97808e-001 5.38068e-001 4 3.05247e+000 0.86455 8.64554e-001 7.30857e-001 6.17836e-001 5 1.11162e+000 0.56010 5.60103e-001 6.47852e-001 7.49348e-001 6 3.68500e-001 0.31972 3.19725e-001 5.70832e-001 1.01916e+000 7 1.07631e-001 0.16776 1.67762e-001 5.24707e-001 1.64112e+000 8 2.85438e-002 0.08505 8.50503e-002 5.06970e-001 3.02197e+000 9 7.25977e-003 0.04268 4.26786e-002 5.01804e-001 5.90009e+000 10 1.82312e-003 0.02136 2.13587e-002 5.00455e-001 1.17261e+001 11 4.56298e-004 0.01068 1.06818e-002 5.00114e-001 2.34150e+001 12 1.14107e-004 0.00534 5.34120e-003 5.00029e-001 4.68113e+001 13 2.85288e-005 0.00267 2.67064e-003 5.00007e-001 9.36133e+001 14 7.13233e-006 0.00134 1.33532e-003 5.00002e-001 1.87222e+002 15 1.78309e-006 0.00067 6.67662e-004 5.00000e-001 3.74441e+002 16 4.45773e-007 0.00033 3.33831e-004 5.00000e-001 7.48882e+002 17 1.11443e-007 0.00017 1.66916e-004 5.00000e-001 1.49776e+003 18 2.78608e-008 0.00008 8.34578e-005 5.00000e-001 2.99553e+003 19 6.96521e-009 0.00004 4.17289e-005 5.00000e-001 5.99105e+003 20 1.74130e-009 0.00002 2.08645e-005 5.00000e-001 1.19821e+004 21 4.35325e-010 0.00001 1.04322e-005 5.00000e-001 2.39642e+004 22 1.08831e-010 0.00001 5.21611e-006 5.00000e-001 4.79284e+004 modifiziertes Newton-Verfahren f(x) = exp(x^2)-1, x_0= 2 k |f(x_k)| x_k |x_k-x_*| conv_lin conv_quad ------------------------------------------------------------------------ 0 5.35982e+001 2.00000 -- -- -- 1 5.35982e+001 1.50916 1.50916e+000 7.54579e-001 3.77289e-001 2 8.75283e+000 0.91448 9.14478e-001 6.05953e-001 4.01517e-001 3 1.30774e+000 0.29481 2.94806e-001 3.22377e-001 3.52525e-001 4 9.07993e-002 0.01245 1.24477e-002 4.22233e-002 1.43224e-001 5 1.54957e-004 0.00000 9.64307e-007 7.74687e-005 6.22353e-003